220 The Rev. J. M. Heath on the Principles of Thermodynamics 



city of the gas below in statical equilibrium. It has generated 

 no motion whatever, although it is a force exercised by a moving 

 body ; but it has neutralized the resistance ; so that they might 

 both of them be at once entirely struck out of the equations of 

 solution, and the problem so converted into a more simple one 

 of the condensation of a gas possessing no elasticity by the action 



of the force 



("'{V- Pl )dv. 



The corrections which this solution supplies to the twoproposi- 

 tions of Mr. Rankine respectively are, that, in the first, it admits 



the generation of heat by the force 1 (P— p x )dv, which Mr. Ran- 

 kine denies ; and in the second it denies the generation of heat 

 by the force I pdv } whichMr. Rankine asserts. I believe my so- 



lution to be right in both instances ; but it is upon the latter 

 point that I anticipate there will be the greatest difficulty of 

 agreement between us, as the appeal is tacitly to a proposition 

 which I think Mr. Rankine will at first sight consider inad- 

 missible. 



In speaking of a gas whose elasticity results from the motion 

 of its particles, Mr. Rankine says, " work done in diminishing 

 the capacity of this vessel wholly takes effect in accelerating the 

 motions of the confined particles." I believe that a gas of this 

 nature may be condensed and its pressure increased (as is re- 

 quired by the law of Mariotte) without increasing the vis viva of 

 the particles, and therefore without altering the heat. 



The pressure at any given point on the surface depends upon 

 the number and frequency of the impacts of the particles, and the 

 vis viva of each of them. We may confine our attention to the 

 impacts of one particle only of a given force. This particle will 

 repeat its impact upon a given spot the more frequently, the 

 shorter the path is which it traverses between two successive im- 

 pulses ; in other words, it will return the more frequently, the 

 more the volume of the gas is contracted. If, therefore, imme- 

 diately after any one appulse of the particle the piston is made 

 to take a new position (still one of rest) immediately below its 

 former position, or to descend through the infinitesimal space do 

 and there remain stationary, the particle will return to it sooner 

 than it would do in its former position. It will strike it and will 

 be reflected by it without any increase of its motion ; in other 

 words, the Pressure may be increased and the Volume contracted 

 without evolution of Heat. 



Liphook, August 11, 1870. 



